Basic Math Examples

((200 \cdot d) + (20 \cdot g) + 7600) ((8000 \div r) \cdot 7) = b

$((200 \cdot d) + (20 \cdot g) + 7600) ((8000 \div r) \cdot 7) = b$

Step 1

Simplify.

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Step 1.1

Combine

8000 \div r

$8000 \div r$ and

7

$7$ .

(200 \cdot d + 20 \cdot g + 7600) \frac{8000 \cdot 7}{r} = b

$(200 \cdot d + 20 \cdot g + 7600) \frac{8000 \cdot 7}{r} = b$

Step 1.2

Multiply

8000

$8000$ by

7

$7$ .

(200 \cdot d + 20 \cdot g + 7600) \frac{56000}{r} = b

$(200 \cdot d + 20 \cdot g + 7600) \frac{56000}{r} = b$

(200 \cdot d + 20 \cdot g + 7600) \frac{56000}{r} = b

$(200 \cdot d + 20 \cdot g + 7600) \frac{56000}{r} = b$

Step 2

Multiply each term in

(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) = b

$(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) = b$ by

\frac{r}{56000}

$\frac{r}{56000}$ to eliminate the fractions.

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Step 2.1

Multiply each term in

(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) = b

$(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) = b$ by

\frac{r}{56000}

$\frac{r}{56000}$ .

(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) \frac{r}{56000} = b \frac{r}{56000}

$(200 \cdot d + 20 \cdot g + 7600) (\frac{56000}{r}) \frac{r}{56000} = b \frac{r}{56000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply

20

$20$ by

g

$g$ .

(200 d + 20 g + 7600) \frac{56000}{r} \frac{r}{56000} = b \frac{r}{56000}

$(200 d + 20 g + 7600) \frac{56000}{r} \frac{r}{56000} = b \frac{r}{56000}$

Step 2.2.2

Simplify terms.

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Step 2.2.2.1

Multiply

$200 d + 20 g + 7600$ by

$\frac{56000}{r}$ .

$\frac{(200 d + 20 g + 7600) \cdot 56000}{r} \cdot \frac{r}{56000} = b \frac{r}{56000}$

Step 2.2.2.2

Cancel the common factor of

$56000$ .

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Step 2.2.2.2.1

Factor

$56000$ out of

$(200 d + 20 g + 7600) \cdot 56000$ .

$\frac{56000 \cdot (200 d + 20 g + 7600)}{r} \cdot \frac{r}{56000} = b \frac{r}{56000}$

Step 2.2.2.2.2

Cancel the common factor.

$\frac{56000 \cdot (200 d + 20 g + 7600)}{r} \cdot \frac{r}{56000} = b \frac{r}{56000}$

Step 2.2.2.2.3

Rewrite the expression.

$\frac{200 d + 20 g + 7600}{r} r = b \frac{r}{56000}$

Step 2.2.2.3

Cancel the common factor of

$r$ .

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Step 2.2.2.3.1

Cancel the common factor.

$\frac{200 d + 20 g + 7600}{r} r = b \frac{r}{56000}$

Step 2.2.2.3.2

Rewrite the expression.

$200 d + 20 g + 7600 = b \frac{r}{56000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine

$b$ and

$\frac{r}{56000}$ .

$200 d + 20 g + 7600 = \frac{b r}{56000}$

Step 3

Move all terms not containing

$d$ to the right side of the equation.

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Step 3.1

Subtract

$20 g$ from both sides of the equation.

$200 d + 7600 = \frac{b r}{56000} - 20 g$

Step 3.2

Subtract

$7600$ from both sides of the equation.

$200 d = \frac{b r}{56000} - 20 g - 7600$

Step 4

Divide each term in

$200 d = \frac{b r}{56000} - 20 g - 7600$ by

$200$ and simplify.

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Step 4.1

Divide each term in

$200 d = \frac{b r}{56000} - 20 g - 7600$ by

$200$ .

$\frac{200 d}{200} = \frac{\frac{b r}{56000}}{200} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

$200$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{200 d}{200} = \frac{\frac{b r}{56000}}{200} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.2.1.2

Divide

$d$ by

$1$ .

$d = \frac{\frac{b r}{56000}}{200} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$d = \frac{b r}{56000} \cdot \frac{1}{200} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.3.1.2

Multiply

$\frac{b r}{56000} \cdot \frac{1}{200}$ .

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Step 4.3.1.2.1

Multiply

$\frac{b r}{56000}$ by

$\frac{1}{200}$ .

$d = \frac{b r}{56000 \cdot 200} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.3.1.2.2

Multiply

$56000$ by

$200$ .

$d = \frac{b r}{11200000} + \frac{- 20 g}{200} + \frac{- 7600}{200}$

Step 4.3.1.3

Cancel the common factor of

$- 20$ and

$200$ .

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Step 4.3.1.3.1

Factor

$20$ out of

$- 20 g$ .

$d = \frac{b r}{11200000} + \frac{20 (- g)}{200} + \frac{- 7600}{200}$

Step 4.3.1.3.2

Cancel the common factors.

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Step 4.3.1.3.2.1

Factor

$20$ out of

$200$ .

$d = \frac{b r}{11200000} + \frac{20 (- g)}{20 (10)} + \frac{- 7600}{200}$

Step 4.3.1.3.2.2

Cancel the common factor.

$d = \frac{b r}{11200000} + \frac{20 (- g)}{20 \cdot 10} + \frac{- 7600}{200}$

Step 4.3.1.3.2.3

Rewrite the expression.

$d = \frac{b r}{11200000} + \frac{- g}{10} + \frac{- 7600}{200}$

Step 4.3.1.4

Move the negative in front of the fraction.

$d = \frac{b r}{11200000} - \frac{g}{10} + \frac{- 7600}{200}$

Step 4.3.1.5

Divide

$- 7600$ by

$200$ .

$d = \frac{b r}{11200000} - \frac{g}{10} - 38$